Question

What are the roots of the polynomial equation x^3-10x=-3x^2+24? Use a graphing calculator and a system of equations.

a. -24, -3, 12
b. -12, 3, 24
c. -4, -2, 3
d. -3, 2, 4

Answer 1

Answer : C

the roots of the polynomial equation x^3-10x=-3x^2+24

We use a graphing calculator

Graph the left hand side expression using graphing calculator

We graph
`y=x^3 - 10x`

Then we graph the right hand side expression using graphing calculator

`y=-3x^2+24`

so we got two system of equations

The intersection of two graphs is our solution

The graph is attached below

We can see that the graph intersects at 3 points

(-4, -24) (-2,12) and (3,-3)

So the roots are -4, -2 , 3

Answer 2

x^3-10x=-3x^2+24
simplifying the above we get
x^3+3x^2-10x-24=0
next we use the graphing tool to solve the expression above:
This will give us:
x=-4,x=-2, x=3
The answer is c] -4,-2,3